State and parameter identification for nonlinear uncertain systems using variable structure theory

  • Fabienne Floret-Pontet
  • Françoise Lamnabhi-Lagarrigue
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 281)


In this paper, we investigate a new identification algorithm grounded on the Variable Structure theory in order to study parameter and state identification for uncertain nonlinear systems in continuous time. On the one hand, we use a specific observer to estimate unknown states of the studied nonlinear system, based on the Variable Structure theory. On the other hand, the well-known chattering property and the invariance properties, characteristic of the Variable Structure theory, make possible the design of the parameter sliding identifier without the use of the additional persisting excitation condition usually required for the input in order to guarantee the parameter convergence. Stability of the state observer, parameter identifiability of the plant and asymptotic convergence of estimated parameters to their nominal values are studied. Finally, we propose some simulations on a pendulum in order to point out the validity of the methodology even if the input u is not persistently exciting. These numerical simulations highlight the robustness of the state and parameter identification with respect to significant parameter uncertainties thanks to the use of the Variable Structure theory.


Nonlinear System State Observer Observation Error Versus Theory Asymptotic Convergence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Fabienne Floret-Pontet
    • 1
  • Françoise Lamnabhi-Lagarrigue
    • 1
  1. 1.Laboratoire des Signaux et des SystèmesC.N.R.S.-SUPELEC-Université de Paris-SudGif-sur-Yvette CédexFrance

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